### Abstract

The author develops a theory of the lattice structure of pseudorandom sequences from shift register generators, i.e., Tausworthe sequences and GFSR (generalized feedback shift register) sequences. The author defines an analog of linear congruential sequences in GF{2,x}, the field of all Laurent series over the Galois field of two elements GF(2), and shows that this class of sequences contains as a subclass the Tausworthe sequence. He derives a theorem that links the k-distribution of such sequences and the successive minima of the k-dimensional lattice over GF{2,x} associated with the sequences, thereby leading to the geometric interpretation of the lattice structure in the k-dimensional unit space of these sequences. This result is generalized to define the successive minima for the point set of k-dimensional vectors each consisting of k consecutive terms of GFSR sequences, and it is shown that GFSR sequences have a similar structure to that of Tausworthe sequences. A simulation problem in which shift-register-type pseudorandom sequences yield useless results due to such lattice structures is discussed.

Original language | English |
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Title of host publication | 90 Winter Simulation Conf. |

Publisher | Publ by IEEE |

Pages | 266-267 |

Number of pages | 2 |

ISBN (Print) | 0911801723 |

Publication status | Published - Dec 1990 |

Externally published | Yes |

Event | 1990 Winter Simulation Conference Proceedings - New Orleans, LA, USA Duration: Dec 9 1990 → Dec 12 1990 |

### Other

Other | 1990 Winter Simulation Conference Proceedings |
---|---|

City | New Orleans, LA, USA |

Period | 12/9/90 → 12/12/90 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Applied Mathematics
- Modelling and Simulation

### Cite this

*90 Winter Simulation Conf.*(pp. 266-267). Publ by IEEE.

**Lattice structure of pseudorandom sequences from shift-register generators.** / Tezuka, Shu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*90 Winter Simulation Conf..*Publ by IEEE, pp. 266-267, 1990 Winter Simulation Conference Proceedings, New Orleans, LA, USA, 12/9/90.

}

TY - GEN

T1 - Lattice structure of pseudorandom sequences from shift-register generators

AU - Tezuka, Shu

PY - 1990/12

Y1 - 1990/12

N2 - The author develops a theory of the lattice structure of pseudorandom sequences from shift register generators, i.e., Tausworthe sequences and GFSR (generalized feedback shift register) sequences. The author defines an analog of linear congruential sequences in GF{2,x}, the field of all Laurent series over the Galois field of two elements GF(2), and shows that this class of sequences contains as a subclass the Tausworthe sequence. He derives a theorem that links the k-distribution of such sequences and the successive minima of the k-dimensional lattice over GF{2,x} associated with the sequences, thereby leading to the geometric interpretation of the lattice structure in the k-dimensional unit space of these sequences. This result is generalized to define the successive minima for the point set of k-dimensional vectors each consisting of k consecutive terms of GFSR sequences, and it is shown that GFSR sequences have a similar structure to that of Tausworthe sequences. A simulation problem in which shift-register-type pseudorandom sequences yield useless results due to such lattice structures is discussed.

AB - The author develops a theory of the lattice structure of pseudorandom sequences from shift register generators, i.e., Tausworthe sequences and GFSR (generalized feedback shift register) sequences. The author defines an analog of linear congruential sequences in GF{2,x}, the field of all Laurent series over the Galois field of two elements GF(2), and shows that this class of sequences contains as a subclass the Tausworthe sequence. He derives a theorem that links the k-distribution of such sequences and the successive minima of the k-dimensional lattice over GF{2,x} associated with the sequences, thereby leading to the geometric interpretation of the lattice structure in the k-dimensional unit space of these sequences. This result is generalized to define the successive minima for the point set of k-dimensional vectors each consisting of k consecutive terms of GFSR sequences, and it is shown that GFSR sequences have a similar structure to that of Tausworthe sequences. A simulation problem in which shift-register-type pseudorandom sequences yield useless results due to such lattice structures is discussed.

UR - http://www.scopus.com/inward/record.url?scp=0025539624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025539624&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025539624

SN - 0911801723

SP - 266

EP - 267

BT - 90 Winter Simulation Conf.

PB - Publ by IEEE

ER -